Alfred Martin

## Answered question

2021-12-08

In the following, simplify using absolute values as necessary.
$\sqrt{3}\left\{216{a}^{6}\right\}$

### Answer & Explanation

turtletalk75

Beginner2021-12-09Added 29 answers

Given information: An expression is given as $\sqrt{3}\left\{216{a}^{6}\right\}$.
Calculations: We have been given an expression is $\sqrt{3}\left\{216{a}^{6}\right\}$.
For finding the odd and even roots by using the absolute value as necessary, we must know about the power property of exponent i.e.
${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$
$⇒\sqrt{3}\left\{216{a}^{6}\right\}$ [Simplify the cube root of $216{a}^{6}$]
$⇒\sqrt{3}\left\{{\left(6{a}^{2}\right)}^{3}\right\}$ [Break the power exponent in the form of ${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$]
$⇒6{a}^{2}$ [$\sqrt{n}\left\{{a}^{n}\right\}=a$, if the value of n is odd.]
Thus, index value of $\sqrt{3}\left\{216{a}^{6}\right\}$ is odd.
Hence, the simplification of

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